Question

. Find zeros of the polynomial p(x)=(x-2 )²- ( x+2)²​

Answer 1

Given,

The polynomial P(x)=(x-2)²-(x+2)² is given.

To find,

The zeroes of the polynomial P(x)=(x-2)²-(x+2)².

Solution,

The zero of the polynomial P(x)=(x-2)²-(x+2)² is 0.

We can simply find the zeroes of the polynomial by equating the polynomial to 0.

P(x)=(x-2)²-(x+2)²

(x-2)²-(x+2)² = 0

Transposing (x+2)² to the right of the equal sign, we get

    (x-2)² =( x+2)²

Using (a-b)² = a²+b²-2ab

and    (a+b)² = a²+b²+2ab

(x²+4-4x) = (x²+4+4x)

    -8x = 0

       x =0

Hence, the zero of the polynomial P(x)=(x-2)²-(x+2)² is 0.